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Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to the point of tangency

Tangent Segment Conjecture

Tangent segments to a circle from a point outside the circle are congruent

Chord Central Angles Conjecture

If two chords in a circle are congruent, then they determine two central angles that are congruent

Chord Arcs Conjecture

If two chords in a circle are congruent, then their intercepted arcs are congruent

Perpendicular to a Chord Conjecture

The perpendicular from the center of a circle to a chord is the bisector of the chord

Chord Distance to Center Conjecture

Two congruent chords in a circle are equidistant from the center of the circle

Perpendicular Bisector of a Chord Conjecture

The perpendicular bisector of a chord passes through the center of the circle

Inscribed Angle Conjecture

The measure of an angle inscribed in a circle is one-half the measure of the intercepted arc

Inscribed Angles Intercepting Arcs Conjecture

Inscribed angles that intercept the same arc are congruent

Angles Inscribed in a Semicircle Conjecture

Angles inscribed in a semicircle are right angles

Cyclic Quadrilateral Conjecture

The opposite angles of a cyclic quadrilateral are supplementary

Parallel Lines Intercepted Arcs Conjecture

Parallel lines intercept congruent arcs on a circle

Tangent Circles

Circles that are tangent to the same line at the same point. They can be internally tangent or externally tangent.

Internally Tangent Circles

Two tangent circles having centers on the same side of their common tangent

Externally Tangent Circles

Two tangent circles having centers on opposite sides of their common tangent

Central Angle

An angle whose vertex is the center of the circle

Inscribed Angle

An angle whose vertex lies on the circle and its sides are chords

Cyclic Quadrilateral

A quadrilateral that can be inscribed in a circle

Secant

A line that intersects a circle in two points